Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 12 0 -2
Translation 3 0 -1
Rotation 3 0 -1
Vibration 6 0 0



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 1 3 4 8
Translation 0 1 1 2
Rotation 0 1 1 2
Vibration 1 1 2 4



Molecule Parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 1
Number of vibrational modes 4





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 1 1 2 3 / 1
Quadratic (Raman) 1 1 2 3 / 1
IR + Raman - - 2 2 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 6 0 0
quadratic 2 21 0 3
cubic 3 56 2 0
quartic 4 126 0 6
quintic 5 252 0 0
sextic 6 462 3 10


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E
linear 1 1 1 2
quadratic 2 5 2 7
cubic 3 10 10 18
quartic 4 24 18 42
quintic 5 42 42 84
sextic 6 83 73 153


Literature




Character tables for chemically important point groups Character table for point group D3 Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement